Introduction

Arik Melikyan
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Arik Melikyan: Institute for Problems in Mechanics, Russian Academy of Science

A chapter in Generalized Characteristics of First Order PDEs, 1998, pp 1-6 from Springer

Abstract: Abstract The classical method of characteristics (MC) was developed for the construction of the solution to nonlinear first order PDE: 0.1 $$ F\left( {x,u,p} \right) = 0,x \in D \subset {\mathbb{R}^n}\left( {p = \frac{{\partial u}}{{\partial x}}} \right) $$ subject to some boundary (initial) conditions specified on a hypersurface M C D: Here u = u(x) is the unknown function of n variables x = (x 1 …,x n ), F 0.2 $$ u\left(x \right) = w\left( x \right),x \in M \subset D $$ is a scalar function (the Hamiltonian).

Keywords: Viscosity Solution; Differential Game; Regular Characteristic; Singular Surface; Tangent Field (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-1758-9_1

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DOI: 10.1007/978-1-4612-1758-9_1

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